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Section: New Results

Algorithms and analysis

Participants : Laurent Alonso, Samuel Hornus.

Data structure for fast witness complexes: Samuel Hornus is currently pursuing work started while a post-doc in Sophia Antipolis, on data structure for the fast construction of witness complexes; these are sub complexes of Delaunay triangulations that can be faster to compute for low dimensional data embedded in high dimensional ambiant space.

Analysis of Boyer and Moore's MJRTY Algorithm: Given a set of $n$ elements each of which is either red or blue, Boyer and Moore's algorithm uses pairwise equal/not equal color comparisons to determine the majority color. We analyze the average behavior of their algorithm, proving that if all $2^n$ possible inputs are equally likely, the average number of color comparisons used is $n-\sqrt{2n/\pi }+O\left(1\right)$ and have variance in $\frac{\pi -2}{\pi }n-\frac{\sqrt{2n}}{\sqrt{\pi }}+O\left(1\right)$. This work has been submitted to SIAM Journal On Computing.